Stepping back to where this started - it might be productive to look a bit wider than just one collector (or one small group of collectors) did.

There are a lot of different ways a piece of folk music might end up with a listener getting the wrong idea of what its original form and context was. Sometimes the problem is with the person publicizing it, sometimes with the listener, sometimes history moves on and background information is lost. There may be many people involved in creating a simple muddle.

I'm thinking here of a examples from Scottish music and klezmer, where we can sometimes trace the same tune for centuries through many different forms. Sometimes the people later in the chain know how they got the piece they're playing and sometimes they don't. Highland pipers often think the versions of "Flowers of the Forest" and "Caller Herrin" they play are just the way the tune is - in fact they are so different from the original as to be barely recognizable. Then there are all the "Irish" tunes that are no such thing; the tune may be unchanged but the backstory is a new invention.

My guess is that folklorists have established a substantial vocabulary to discuss this sort of thing - one term like "mediation" won't cut it.